Block #74,237

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/21/2013, 10:04:30 AM · Difficulty 8.9954 · 6,725,024 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

7182e21b4eac1c323b2e9f64956288314544523619cd2f50d84412f2455cbfd0

View on Chainz ↗

Height

#74,237

Difficulty

8.995376

Transactions

Size

203 B

Version

Bits

08fed0ef

Nonce

166

Timestamp

7/21/2013, 10:04:30 AM

Confirmations

6,725,024

Mined by

⛏️ P2SHAawzRYLpHU7wZxoYUFawXzGZd4NJSmHiTJ

Merkle Root

93c762309f2fe8a5146bb2a0978befb3fb61787c1e8a5c36817d32256a29d427

Transactions (1)

Coinbase93c762309f2fe8…7d32256a29d427

1 in → 1 out12.3400 XPM110 B

AawzRYLp…NJSmHiTJ

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

3.393 × 10¹⁰¹(102-digit number)

33930594054120709298…68949548748437980359

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

3.393 × 10¹⁰¹(102-digit number)

33930594054120709298…68949548748437980359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.393 × 10¹⁰¹(102-digit number)

33930594054120709298…68949548748437980361

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

6.786 × 10¹⁰¹(102-digit number)

67861188108241418596…37899097496875960719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.786 × 10¹⁰¹(102-digit number)

67861188108241418596…37899097496875960721

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

1.357 × 10¹⁰²(103-digit number)

13572237621648283719…75798194993751921439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.357 × 10¹⁰²(103-digit number)

13572237621648283719…75798194993751921441

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

2.714 × 10¹⁰²(103-digit number)

27144475243296567438…51596389987503842879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.714 × 10¹⁰²(103-digit number)

27144475243296567438…51596389987503842881

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

5.428 × 10¹⁰²(103-digit number)

54288950486593134877…03192779975007685759

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★☆☆☆☆

Rarity

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer